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Deviations from Ohm's Law in Weak Electrolytes

### Abstract

The effect of an external electric field on the electrolyticdissociation is computed kinetically from the equations for Brownian motion in the combined Coulomb and external fields. The result is an increase of the dissociation constant, by the factor *K*(*X*)/*K*(0) = *F*(*b*) = 1+*b*+(1/3)*b* ^{2}..., where the parameter *b* is proportional to the absolute value of the field intensity, and inversely proportional to the dielectric constant. In water at 25°, *F*(*b*) = *F*(1) = 2.395 for a field of 723 kilovolt/cm, while in benzene, the same increase of the dissociation constant is obtained for a field of only 21 kilovolt/cm. The theory is quantitatively confirmed by the deviations from Ohm's law which have been observed for solutions of weak electrolytics in water and in benzene. For solutions of salts in acetone, and for solidelectrolytes such as glass, mica, celluloid, etc., the observed increments of conductance are smaller than those expected from the theory, but still of the predicted type and order of magnitude. The kinetic constants of dissociation and recombination can be computed separately on the assumption that the recombination proceeds as rapidly as the mutual approach of two ions due to the Coulomb attraction. The derivation is equivalent to that of Langevin, and leads to the same result. In the Langevin case, the coefficient of recombination is independent of the field; that of dissociation is increased by the factor *F*(*b*). Slower reactions may occur when a (chemical) rearrangement of the ion pairs is involved. In the most general case, it is necessary to consider the successive reversible reactions*ions*⇄*pairs*⇄*molecules,* where the former takes place with the Langevin velocity; only the reaction rate *pairs*→*ions* depends on the field. On the basis of this picture, the saturation phenomena observed in dielectrics are discussed in relation to the field effect.

© 1934 American Institute of Physics

Received 29 May 1934
Published online 03 November 2004